Subgroups — #14561691

Order 2432.

86 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#11926949	C₂	1	1	yes	maximal, characteristic
2	C₄⋊(C₁₉⋊C₁₆)	C₂	1	1	yes	maximal, characteristic
3	C₁₉×#335	C₂	1	1	yes	maximal, characteristic
4	#10597315	—	2	1	no	—
5	C₁₉×C₄⋊C₈	—	2	1	no	—
6	C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
7	#10597275	—	2	1	no	—
8	#10597275	C₄	1	2	yes	—
9	C₂×C₁₉⋊C₁₆	—	2	1	no	—
10	C₂×Dic₃₈	—	4	1	no	—
11	C₂×C₈×C₁₉	—	4	1	no	—
12	C₂×C₈×C₁₉	C₂×C₄	1	1	yes	characteristic
13	C₂×C₈×C₁₉	D₄	1	1	yes	characteristic
14	C₄²×C₁₉	D₄	1	1	yes	characteristic
15	C₄⋊Dic₁₉	—	2	2	no	—
16	C₄⋊Dic₁₉	—	4	1	no	—
17	C₁₉⋊C₁₆	—	4	1	no	—
18	C₂×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
19	C₂×C₄×C₁₉	D₈	1	1	yes	characteristic
20	C₂×C₄×C₁₉	SD₁₆	1	1	yes	characteristic
21	C₂×Dic₁₉	—	4	2	no	—
22	Dic₃₈	—	8	1	no	—
23	Dic₃₈	—	8	1	no	—
24	C₈×C₁₉	—	2	1	no	—
25	C₈×C₁₉	—	8	1	no	—
26	C₈×C₁₉	SD₁₆	1	1	yes	characteristic
27	C₈×C₁₉	Q₁₆	1	1	yes	characteristic
28	#1364	—	19	1	no	maximal, Sylow
29	C₂²×C₁₉	#102	1	1	yes	characteristic
30	C₄×C₁₉	—	2	1	no	—
31	C₄×C₁₉	#101	1	1	yes	characteristic
32	C₄×C₁₉	#103	1	1	yes	characteristic
33	C₄×C₁₉	D₁₆	1	1	yes	characteristic
34	C₄×C₁₉	SD₃₂	1	1	yes	characteristic
35	Dic₁₉	—	8	2	no	—
36	#500	—	19	1	no	—
37	C₄⋊C₁₆	—	19	1	no	—
38	#335	D₁₉	1	1	yes	characteristic
39	C₂×C₁₉	#332	1	1	yes	characteristic
40	C₂×C₁₉	#357	1	1	yes	characteristic
41	C₂×C₁₉	#362	1	1	yes	characteristic
42	C₄⋊Q₈	—	38	1	no	—
43	C₂×C₁₆	—	38	1	no	—
44	#107	—	19	2	no	—
45	#107	—	38	1	no	—
46	C₄⋊C₈	—	2	1	no	—
47	C₄×C₈	C₂×D₁₉	1	1	yes	characteristic
48	C₁₉	#1364	1	1	yes	characteristic, complemented, Sylow
49	C₂×Q₈	—	76	1	no	—
50	C₂×C₈	—	4	1	no	—
51	C₂×C₈	C₄×D₁₉	1	1	yes	characteristic
52	C₂×C₈	D₇₆	1	1	yes	characteristic
53	C₄⋊C₄	—	38	2	no	—
54	C₄⋊C₄	—	76	1	no	—
55	C₄²	C₂²⋊D₁₉	1	1	yes	characteristic
56	C₁₆	—	76	1	no	—
57	Q₈	—	152	1	no	—
58	Q₈	—	152	1	no	—
59	C₂×C₄	—	76	2	no	—
60	C₂×C₄	(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
61	C₂×C₄	#64525	1	1	yes	characteristic
62	C₂×C₄	#64527	1	1	yes	characteristic
63	C₈	—	2	1	no	—
64	C₈	—	8	1	no	—
65	C₈	#64516	1	1	yes	characteristic
66	C₈	Dic₇₆	1	1	yes	characteristic
67	C₂²	#10597266	1	1	yes	characteristic
68	C₄	—	2	1	no	—
69	C₄	—	152	2	no	—
70	C₄	#10597273	1	1	yes	characteristic
71	C₄	#10597281	1	1	yes	characteristic
72	C₄	#10597283	1	1	yes	characteristic
73	C₄	#10597285	1	1	yes	characteristic
74	C₂	#11926291	1	1	yes	characteristic
75	C₂	#11926344	1	1	yes	characteristic
76	C₂	#11926359	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	#10597266
commutator	C₂×C₈×C₁₉	C₂×C₄
Frattini	C₄×C₈	C₂×D₁₉
Fitting	C₁₉×#335	C₂
socle, prime radical	C₂²×C₁₉	#102
cosocle	C₄×C₈×C₁₉	C₂²
hypercenter	#335	D₁₉
hypocenter	C₁₉	#1364
LCS	G ▷ C₂×C₈×C₁₉ ▷ C₂×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₄×C₈ ◁ #335

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
48. C₁₉	#1364	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
#11926949	2
C₄⋊(C₁₉⋊C₁₆)	2
C₁₉×#335	2
#1364	19